Abstract: The group of i?-homomorphisms Horn* (ikf, A), where Λf, A are modules over a ring R, is, in a natural way, a module over the endomorphism ring S of M.Under certain weak assumptions on M, the following is true: Hom Λ (M, -) carries injective envelopes of ϋN modules into injective envelopes of &-modules iff M generates all its submodules.Modules of the latter type are called self-generators.For M a selfgenerator, Horn* (ikf, -) has additional properties concerning chain conditions and the socle.Many of the known results in this area, in particular those for M projective, are special cases of our main theorems.